Actuated Linear Motion Axis

I ordered a cheap leadscrew assembly intended for low-cost 3D printers from Amazon. The leadscrew came with a brass flanged lead nut, a pair of ball bearings mounted in zinc blocks, and a flexible coupling that fits the NEMA 17 motor output shaft. The leadscrew has a diameter of 8 mm, a pitch of 2 mm, and 4 starts. This means it has an overall lead of 8 mm/rev.

A quick note about running leadscrews directly in bearing bores: conventional engineering wisdom states that it is a bad idea to run threaded rods in bearings because of small load-bearing area results in high stresses. This is still true for leadscrews, but the trapezoidal threadform retains the major diameter across the width of its lands, making it less problematic to run them in bearing bores compared to “standard” fastener threadforms which are triangular and taper to an acute angle.

Repeatability Testing

Actuated Linear Motion Axis Test from Shien Yang Lee on Vimeo.

I tested the repeatability of the actuated linear motion axis in two ways.

Repeatability along motion axis

First, I repeated the “straightness” test I carried out last week for the linear axis without the actuator.After running the carriage back and forth between its extreme positions 8 times, I got a group of laser projection points with the maximum spread of 15 mm at a distance of 2.9 m. This translates to a side-to-side angular error of 0.3°, which is a ~75% improvement from the 1.29° measured on the non-actuated axis. I think there are two factors contributing to this improvement.

First, the motor and leadscrew is able to repeat axial position better than I could by hand. This places the carriage closer to the same locations when each measurement is taken. This theory is supported by the observation that points measured at each position (X0 vs. X100) all lay within 5 mm of each other (angular uncertainty of <0.1°). This suggests that most of the error measured comes from global straightness and parallelism errors in the box way instead of local “wiggling” of the slider.

Second, the leadscrew provides a degree of preload to take up part of the radial clearance. I drilled the slider for the lead nut using a portable drill and did not make the hole perfectly square to the faces of the slider. This slight misalignment places the simply-supported leadscrew (I left it floating in the bearing on the non-driven side) under bending, causing it to act as a preload spring. However, as we learned in class, this is not a good preload configuration since the system’s stiffness varies according to the square of carriage’s distance from one end.

Repeatability orthogonal to motion axis

My second repeatability test was aimed at measuring the precision with which the actuator can move the carriage to a specified position. I attached my laser pointer to the carriage orthogonally, such that it projected a beam perpendicular to the direction of motion. For the adjustable standing desk, this is the sensitive direction.

I recorded the position of the projected beam across the 100 mm-long travel of the carriage on 10-mm intervals. The repeatability at each position was within 1 mm. Note that we are now measuring axial displacement instead of angular error, so using a laser pointer conferred no resolution advantage.

More interestingly, I observed the effects of backlash in this test. I moved the carriage to each position in the following sequence:

0 > 100 > 10 > 90 > 20 > 80 > 30 > 70 > 60 > 40 > 50

Each reversal in direction caused the distance traveled to be short by approximately 1 mm. This is consistent with the perceptible backlash in the low-quality lead nut.

PUPS 4: Groove KC Model

1.

Please see  Update: Kinematic Coupling for my latest work on the groove KC model. In summary, I constructed an updated model from machined plywood and hardened steel contact elements (dowel pins and steel balls).

2.

Stiffness

This metric was the most challenging to measure. Without access to precise inspection equipment, I resorted to placing dead weights such as a 100-g bag of fasteners on the KC and attempting to measure deflection using a laser pointer. This yielded no perceptible motion at a distance of 2.9 m. I attribute this to two reasons:

  1. I placed the weight above the center of the coupling circle, which would have resulted in deflection along the vertical axis. To the first order, this is not expected to cause any rotational error — making our Abbe error-based measurement scheme moot.
  2. My design is predicted to have an RMS stiffness of 62 N/micron. Since my dead weight only applied a force of less than 1 N, the predicted deflection would be far too small to measure using my methods.

The Makerworkshop will be commissioning an Instron UTS in the coming weeks, and I plan to repeat this test using the machine once it comes online.

Repeatability

Please see Update: Kinematic Coupling for repeatability test results. In summary, I measured 0.04° of angular for my KC.

Accuracy

I designed the top and bottom faces of my KC to be 28.95 mm apart. The actual stack was measured to be 29.0 mm thick. I was impressed by how close I got, considering that the plywood rounds were machined on a less-than-stiff CNC router with a relatively worn-out sacrificial bed. In any case, we know the three-groove KC is quite robust against small inaccuracies and this is borne out in the repeatability test results.

3.

I am yet to quantify this, but I believe the actual apparent stiffness of my KC would be significantly lower than the value predicted by the spreadsheet. The original spreadsheet predictions only considered the interface materials. In my case, I predict that the majority of the deflection would come from the plywood support structure instead of the hardened steel contact elements. If I had to make KC’s for my table, I would update the spreadsheet to account for the plate bending that occurs within the coupling circle when the coupling is centrally loaded.